A Simple Method for In Situ Determination of Linear Thermal Expansion Coefficients of Thin Films
Abstract This work presents a simple method for determination of linear thermal expansion coefficients (LTEC) of thin films with a compact microstructure. The microstructure comprises of a pair of cantilever beams with different lengths connected by a short tip. By heating the microstructure, the thermal strain causes two beams to deflect each other, thereby magnifying the deflection, which is measured by the tip directly under an optical microscope with the specimen placed in a heating stage. An analytical model is derived to relate the measured displacement to thermal strain, therefore, LTEC of thin films can be calculated. The analytical model is free from any correction factor. Furthermore, the accuracy of LTEC measurement is significantly enhanced because the measured displacement is independent of some physical values, namely the Young’s modulus, Poisson’s ratios and thickness of the substrate and the thin film, and the LTEC of the substrate. Finite element model is also used to support the analytical model and to perform nonlinear analysis. Experimental results with SiO2 films as well as undoped LPCVD polysilicon films are used herein to demonstrate the effectiveness of the proposed method.